1. **State the problem:** Solve for $x$ in the equation $$\frac{6.11 + x}{5} = 152.4.$$\n\n2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 5 to eliminate the denominator. This uses the property that if $\frac{a}{b} = c$, then $a = b \times c$.\n\n3. **Multiply both sides by 5:**\n$$6.11 + x = 5 \times 152.4$$\n\n4. **Calculate the right side:**\n$$5 \times 152.4 = 762$$\n\n5. **Rewrite the equation:**\n$$6.11 + x = 762$$\n\n6. **Isolate $x$ by subtracting 6.11 from both sides:**\n$$x = 762 - 6.11$$\n\n7. **Calculate the subtraction:**\n$$x = 755.89$$\n\n**Final answer:** $x = 755.89$